On a parabolic problem with nonlinear term in a half space and global behavior of solutions

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• 作者：Habib Mâ ; agli ; Syrine Masmoudi ; Malek Zribi
• 关键词：Parabolic equation ; Positive solutions ; Green function
• 刊名：Journal of Differential Equations
• 出版年：2009
• 出版时间：1 May 2009
• 年：2009
• 卷：246
• 期：9
• 页码：3417-3447
• 全文大小：273 K

文摘

We take up the existence and global behavior of positive continuous solutions of the following nonlinear parabolic equation in (n2) with boundary conditions u=0 on and u(x,0)=u₀(x). The nonlinear term is required to satisfy some conditions related to a functional class , which we introduce in this paper and will be called parabolic Kato class in the half space. Our approach is based on potential theory.